Related papers: Positive Kernels and Quantization
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a…
An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…
In this paper, we study $k$-positivity and Schmidt number under standard orthogonal group symmetries. The Schmidt number is a natural quantification of entanglement in quantum information theory. First of all, we exhibit a complete…
We introduce a non commutative analog of the Bohr compactification. Starting from a general quantum group G we define a compact quantum group bG which has a universal property such as the universal property of the classical Bohr…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…
A brief exposition of the general theory of characteristic classes of quantum principal bundles is given. The theory of quantum characteristic classes incorporates ideas of classical Weil theory into the conceptual framework of…
With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…
In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant {\Lambda} and try to make contact with alternative quantization approaches already…
In this paper we prove a generalization of a theorem of Schneider, which gives a criterion for a projective surface over the complex numbers to have an ample cotangent bundle. After reviewing different notions of positivity, we introduce a…
By the quantization condition compact quantizable Kaehler manifolds can be embedded into projective space. In this way they become projective varieties. The quantum Hilbert space of the Berezin-Toeplitz quantization (and of the geometric…
We study positive kernels on $X\times X$, where $X$ is a set equipped with an action of a group, and taking values in the set of $\mathcal A$-sesquilinear forms on a (not necessarily Hilbert) module over a $C^*$-algebra $\mathcal A$. These…
The paper introduces a new characterisation of strictly positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…